MADISON, Wis. — Gov. Scott Walker has cited his experience battling unions here four years ago as proof that voters appreciate a political leader willing to “go big and go bold.”

So as he woos supporters around the country for a possible presidential bid, Walker (R) is once again picking a fight against a powerful institution at home — public universities.

Walker’s new budget proposal would slash $300 million from the University of Wisconsin system over the next two years. That’s a 13 percent reduction in state funding.

The cut, Walker said, is a fair exchange for a two-year tuition freeze and new flexibility long sought by administrators to set pay scales and campus construction priorities. But the plan is drawing angry responses from school officials and students as the state’s Republican-led legislature takes it up.

Walker drew a direct line between his 2011 battle against his state’s public-sector unions, which sparked mass protests and made him a national GOP star, and his new quest to transform higher education.

“It’s very much like what we did four years ago,” he said last week during a trip to London, which was billed as a trade mission but was widely seen as a move by Walker to gain some foreign policy expertise.

It is unusual for a governor pondering a presidential run to take on what could be an all-consuming political brawl at home — and a distraction from the coast-to-coast travel and fundraising required to build a national campaign.

But the university budget debate has a clear upside for Walker, who is shaping his political brand around the idea that he does not shy away from a fight. Whether or not he succeeds in transforming the universities, the battle itself, coming in the midst of Walker’s effort to rise above a crowded field of prospective Republican presidential candidates, is likely to play well with conservative voters who see universities as elite institutions and hotbeds of left-leaning activism.

In Wisconsin, university advocates say their schools could be a far more difficult target for Walker, with a broader and deeper base of support than the unions had.

Hundreds of students and faculty members protested on campuses last weekend, and organizers said that was only the beginning. Officials from the state’s flagship campus in Madison have begun to tap into the school’s large network of alumni and other supporters to encourage opposition to Walker’s plan.

A harbinger of what Walker might face came in an immediate uproar on social media this month after his staff proposed changing the university’s ethereal focus on the pursuit of truth, known as the “Wisconsin Idea,” to a grittier focus on “workforce needs.”

Critics charged that Walker, who did not graduate from college, was disrespecting the traditions of the University of Wisconsin. Walker immediately backed off and described the change as a mistake.

Still, Rebecca Blank, chancellor of the Madison campus, emphasized protecting university traditions as part of a letter she sent to 160,000 alumni. It urged alumni to lobby their local lawmakers “so that we can continue to provide Wisconsin students with an outstanding education, and serve the state in the best tradition of the Wisconsin Idea.”

Michael Fahey, managing director of the UW-Madison alumni association, said he is reaching out to the university’s 400,000 alums around the world.

“We know that Wisconsin alumni represent the full spectrum of political opinions, but we have been pleased that alumni are eager to lend their voice to the campaign,” Fahey said.

In his remarks in London, Walker predicted that his proposed changes to universities would lead to the same kind of improvements that his 2011 law brought about in K-12 schools and local governments. Curbing collective bargaining for most public-sector unions, a core piece of that law, gave officials more freedom to operate efficiently and effectively, he said.

And he noted that, just as his children attended public schools back then, he has a personal stake in the university system today, with a son attending UW-Madison.

“People said [the 2011 law] would be the death of public education in my state,” Walker said. “Back then I had two kids in public high schools, and I said I have a vested interest then, just like I do now in the UW system. . . . With our authority, the same thing will happen with the University of Wisconsin system.”

Walker aides said the proposed budget cuts are part of his philosophy of reforming government rather than raising taxes or merely cutting spending.

Laurel Patrick, a Walker spokeswoman, said the governor’s proposal would give university officials much of what they have wanted. “For years, administrators at the University of Wisconsin have said that getting out from under the bureaucracy of state government would allow them to achieve considerable savings in areas like purchasing, construction and hiring,” she said.

Democrats say Walker is putting his national ambitions ahead of state needs. Besides the university cuts, they note that his budget plan includes other items popular with conservatives, such as drug testing for public benefits, expanded K-12 vouchers and less money for public broadcasting.

State Sen. Jennifer Shilling (D), the Senate minority leader, said the state budget proposal “looks like a presidential document.”

Although Shilling said she does not expect protests as large as those in 2011, she said that “more people will find themselves in the crosshairs with his budget. Don’t underestimate the intelligence of Wisconsinites: They know this is fodder for a presidential campaign.”

University administrators have been blunt in their criticism of the governor, while other advocates have sought to build grass-roots opposition to the plan.

In a public meeting last week with hundreds of faculty members, students and staffers, Blank, the UW-Madison chancellor, said the cuts would undoubtedly lead to higher tuition for out-of-state students.

“There will surely be layoffs,” she said as some audience members groaned. “These cuts are too big too handle. They’re too big for the university and too big for the state.”

In rural communities, an e-mail chain initiated by the state’s teachers union encourages residents to put green lights outside their homes to show their support for the university. On Saturday, more than 300 students protested in single-digit temperatures. One person held a sign referring to the school’s mascot that read: “The Wisconsin Badger is an Endangered Species.”

Eleni Schirmer, a fourth-year graduate student who helps lead the teaching-assistant associations, said the budget cuts represent another epochal time for the university. She was in her first year when Capitol Square in Madison filled with protesters, and she said she became so fascinated that studying unions became part of her graduate work. She said activists are reinvigorated.

“Walker’s pretty bold,” she said. “If he has presidential aspirations, we’re going to show what he is willing to put at stake to get there, and that is the life of the university.”

Ray Cross, the president of the university system, which includes 13 four-year schools and 13 two-year schools, said the possible cuts came as a disappointment. He had proposed a $95 million increase in funding. Cross said he and his staff have been poring over budget documents and spreadsheets to find cuts. He said he wants to assess multiple scenarios before determining how bad downsizing could be, for fear of “crying wolf.”

Walker’s team has played down the impact, saying the cuts would amount to a 2.5 percent reduction in the university system’s $6 billion budget. Walker has suggested increasing professors’ workloads to help make up the difference.

“We didn’t know the details until a few days before the budget was released,” Cross said. “We are going to be a dramatically different organization at the end of this. It is a statement from the state that ‘we want you to be smaller, a more streamlined organization.’ ”

Still, Cross could not hide his frustration. Looking out his 17th-floor window from the university administration building, up the street from the state Capitol, he joked: “Sometimes I want to throw water on it.”